Probability distributions for polymer translocation

TL;DR

This study investigates the dynamics of self-avoiding polymer translocation through a membrane pore in two dimensions, revealing universal scaled distributions and sub-diffusive behavior of the translocation coordinate.

Contribution

It provides numerical measurements of translocation time and coordinate distributions, highlighting their scaling properties and non-trivial shapes for polymers in 2D.

Findings

Scaled translocation time distribution is exponential for large T.

Translocation coordinate distribution is Gaussian at short times with sub-diffusive variance.

Non-trivial stable shape of P(s,t) for T > mean translocation time.

Abstract

We study the passage (translocation) of a self-avoiding polymer through a membrane pore in two dimensions. In particular, we numerically measure the probability distribution Q(T) of the translocation time T, and the distribution P(s,t) of the translocation coordinate s at various times t. When scaled with the mean translocation time <T>, Q(T) becomes independent of polymer length, and decays exponentially for large T. The probability P(s,t) is well described by a Gaussian at short times, with a variance that grows sub-diffusively as t^{\alpha} with \alpha~0.8. For times exceeding <T>, P(s,t) of the polymers that have not yet finished their translocation has a non-trivial stable shape.